Selecting copy sections on iPad

Sometimes when I select text, the iPad decides I want to select an entire section of a document, and it can make it difficult to shrink the the selection box down to just select the word(s) I actually want to copy. When I drag a side of the selection box inwards, it often just pops back into place after I release it. Sometimes one side will stay in place, then I can move the others, but other times I can't shrink the selection box at all, and I just have to retry the selection or give up and us my organic cache memory (which becomes less reliable with each passing day) and my fingers (which thankfully are still holding up pretty well). Are there any tricks for selecting words when the iPad prefers sections?

I generally don't have this problem. I also usually double tap on the first word I want to highlight in the selection and then use the drag points to get everything I need. Does it happen in some applications more than another?

My impression is that it happens more in web pages, but I spent yesterday playing around with it, and seemed to get most in e-books, particularly in iBooks. I figured it would be a common problem, but since it's not, I'll try to find an easy-to-duplicate example.